In England you have to fence your own stock in. In Scotland generally the cost is deemed to be 50:50. However if one side is a garden or somewhere with no stock ever and the other has the stock then morally they should pay the lions share. ie at least the cost of increasing a fence which marks a boundary (couple of lines of wire and some posts split 50:50 cost wise up to a proper stock proof standard.
Currently if your dog attacks your own stock on your own land, no offence is committed, although that might change with the changes in rules on dogs being considered.
If the animals arent yours, and shouldnt be there, having broken in then it is a moot point, I would certainly be strongly resisting any claim for compensation if for eg it was a garden they broke into, whereas if it were fields the dog was roaming then there might be more argument that the dog wasnt under control.